Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
764 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C137 |
| prime radical | #3006×C137 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3007×C137 | C2 | semidirect |
| 3. #2816×C137 | C2 | semidirect |
| 4. #1782×C137 | C2 | semidirect |
| 5. #1511×C137 | C2 | semidirect |
| 6. #1510×C137 | C2 | semidirect |
| 7. #1306×C137 | C2 | semidirect |
| 255. #9981 | C137 | direct (N × H) |
| 256. C137 | #9981 | direct (N × H) |
| 257. #3007 | C2×C137 | semidirect |
| 259. #2816 | C2×C137 | semidirect |
| 260. #1782 | C2×C137 | semidirect |
| 261. #1511 | C2×C137 | semidirect |
| 262. #1510 | C2×C137 | semidirect |
| 263. #1306 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3007×C137 | 2 |
| #3006×C137 | 2 |
| #2816×C137 | 2 |
| #1782×C137 | 2 |
| #1511×C137 | 2 |
| #1510×C137 | 2 |
| #1306×C137 | 2 |
| #9981 | 137 |